U.S. patent number 6,703,835 [Application Number 10/119,724] was granted by the patent office on 2004-03-09 for system and method for unwrapping phase difference images.
This patent grant is currently assigned to GE Medical Systems Global Technology Co. LLC. Invention is credited to Joseph K. Maier, Graeme C. McKinnon, Sandhya Parameswaran, Sarah K. Patch, Tejaswini Shubhachint.
United States Patent |
6,703,835 |
Patch , et al. |
March 9, 2004 |
System and method for unwrapping phase difference images
Abstract
A method for processing digital images includes acquiring a
phase difference image which includes one or more phase wraps,
creating a modulated phase difference image from the phase
difference image, comparing the modulated phase difference image to
the phase difference image to locate areas in the phase difference
image to be unwrapped, and unwrapping the phase difference image
based on the areas located in the comparing step. The unwrapping
step is performed by replacing wrapped pixels in the phase
difference image with pixels in the modulated phase difference
image plus an integer multiple of .pi.. The integer multiplier is
computed by comparing overlapping pixels in the image segments.
This has a smoothing effect causing the wrapped pixels in the phase
difference image to become unwrapped. As a result of this pixel
replacement process, an image of improved quality and information
content is produced compared with conventional methods.
Inventors: |
Patch; Sarah K. (Milwaukee,
WI), Shubhachint; Tejaswini (Waukesha, WI), McKinnon;
Graeme C. (Hartland, WI), Parameswaran; Sandhya (Gurnee,
IL), Maier; Joseph K. (Milwaukee, WI) |
Assignee: |
GE Medical Systems Global
Technology Co. LLC (Waukesha, WI)
|
Family
ID: |
28789972 |
Appl.
No.: |
10/119,724 |
Filed: |
April 11, 2002 |
Current U.S.
Class: |
324/307 |
Current CPC
Class: |
G01R
33/565 (20130101); G01R 33/3875 (20130101); G01R
33/56527 (20130101); G01R 33/56563 (20130101) |
Current International
Class: |
G01R
33/54 (20060101); G01R 33/565 (20060101); G01R
33/38 (20060101); G01R 33/3875 (20060101); G01N
003/00 () |
Field of
Search: |
;324/307,309,314
;382/100,103,131 ;600/410,411 |
References Cited
[Referenced By]
U.S. Patent Documents
Other References
M Chrobak, C. Durr, G. Woegi, et al. Correcting Phase Wraps in MRI
Images in the Presence of Errors, preprint received Dec. 29, 2000.
.
Li An, Qing-San Xiang, and Sofia Chavez, "A Fast Implementation of
The Minimum Spanning Tree Method for Phase Unwrapping," IEEE
Transactions on Medical Imaging, vol. 19, No. 8, pp. 805-808,
(200). .
M. Hedley, D. Rosenfeld, "A New Two-Dimensional Phase Unwrapping
Algorithm for MRI Images," Magnetic Resonance in Medicine, vol. 24,
pp. 177-181, (1992). .
S.M. Song, S. Napel, N.J. Pelc, G.H. Glover, "Phase Unwrapping of
MR Images Using Poisson Equation," IEEE Transactions on Image
Processing, pp. 667-676, (1995). .
S.M. Song, S. Napel, N.J. Pelc, G.H. Glover, "A Least Squares Based
Phase Unwrapping Algorithm for MRI," IEEE TMI, pp. 1784-1788,
(1994). .
J. Strand, T. Taxt, "Performance Evaluation of Two-dimensional
Phase Unwrapping Algorithms," Applied Optics vol. 38 No. 20, pp.
4333-4344, (1999). .
E. Schneider, G.H. Glover, "Rapid In-vivo Proton Shimming,"
Magnetic Resonance in Medicine vol. 18, pp. 335-347, (1991). .
N.H. Ching, D. Rosenfeld, M. Braun,"Two-Dimensional Phase
Unwrapping Using a Minimum Spanning Tree Algorithm," IEEE
Transactions On Image Processing, vol. 1, No. 3, pp. 355-365,
(1992)..
|
Primary Examiner: Gutierrez; Diego
Assistant Examiner: Vargas; Dixomara
Attorney, Agent or Firm: Miles & Stockbridge P.C.
Kondracki; Edward J.
Claims
We claim:
1. A method for processing digital images, comprising: acquiring a
phase difference image which includes one or more wraps; creating a
modulated phase difference image from said phase difference image;
comparing said modulated phase difference image to said phase
difference image to locate overlapping areas in said phase
difference image to be unwrapped; and unwrapping said phase
difference image based on the overlapping areas located in said
comparing step.
2. The method of claim 1, wherein said phase difference image is a
magnetic resonance image.
3. The method of claim 2, wherein said magnetic resonance image is
an image derived from an open MRI system.
4. The method of claim 1, wherein said phase difference image is an
X-ray image.
5. The method of claim 1, wherein said phase difference image is an
ultra-sound image.
6. The method of claim 1, wherein said phase difference image
derives from a synthetic aperture radar system.
7. The method of claim 1, wherein said creating step includes:
rotating said phase difference image by a predetermined angle.
8. The method of claim 7, wherein said creating step further
includes: registering the pixels in said rotated phase difference
image so that values of said pixels lie within a desired phase
range, said registered phase difference image corresponding to said
modulated phase difference image.
9. The method of claim 8, wherein said desired phase range equals a
phase range within which pixels of said phase difference image
reside.
10. The method of claim 7, wherein said rotating step includes
rotating said phase difference image in accordance with the
following equation:
wherein .phi..sub.mod is said modulated phase difference image,
.phi. is said phase difference image, and .theta. is a
predetermined angle of rotation.
11. The method of claim 10, wherein .theta. lies between 0 and
2.pi..
12. The method of claim 10, wherein .theta. is .pi..
13. The method of claim 1, wherein said comparing step includes:
defining image segments in said phase difference image; defining
image segments in said modulated phase difference image; and
determining areas where the image segments in said phase difference
image overlap the image segments in said modulated phase difference
image.
14. The method of claim 13, wherein said first defining step
includes: masking out pixels located near said one or more wraps of
said phase difference image to yield said image segments; and
wherein said second defining step includes: masking out pixels
located near said one or more wraps of said modulated phase
difference image to yield said image segments.
15. The method of claim 1, wherein said unwrapping step includes:
replacing pixels in said overlapping areas of said phase difference
image with pixels in said modulated phase difference image plus an
integer multiple of .pi..
16. The method of claim 15, further comprising: computing said
integer multiple of .pi. as a function of the average difference
between values of pixels in said phase difference image and pixels
in said modulated phase difference image.
17. A system for processing digital images, comprising: a storage
unit which stores a digital image; and a processor for processing
the digital image under control of a computer program, said
processor: (a) generating a phase difference image from the digital
image, said phase difference image including one or more wraps, (b)
creating a modulated phase difference image from said phase
difference image, and (c) comparing said modulated phase difference
image to said phase difference image to locate overlapping areas in
said phase difference image to be unwrapped, and (d) unwrapping
said phase difference image based on the overlapping areas located
in (c).
18. The system of claim 17, wherein the digital image is a magnetic
resonance image.
19. The system of claim 18, wherein the magnetic resonance image is
an image derived from an open MRI system.
20. The system of claim 17, wherein the digital image is an X-ray
image.
21. The system of claim 17, wherein the digital image is an
ultra-sound image.
22. The system of claim 17, wherein the digital image is a
synthetic aperture radar system.
23. The system of claim 17, wherein said processor creates said
modulated phase difference image by rotating said phase difference
image by a predetermined angle.
24. The system of claim 23, wherein said processor rotates said
phase difference image in accordance with the following
equation:
wherein .phi..sub.mod is said modulated phase difference image,
.phi. is said phase difference image, and .theta. is a
predetermined angle of rotation.
25. The system of claim 24, wherein .theta. lies between 0 and
2.pi..
26. The method of claim 24, wherein .theta. is .pi..
27. The system of claim 23, wherein said processor registers pixels
in said rotated phase difference image so that values of said
pixels lie within a desired phase range, said registered phase
difference image corresponding to said modulated phase difference
image.
28. The system of claim 27, wherein said desired phase range equals
a phase range within which pixels of said phase difference image
reside.
29. The system of claim 17, wherein said processor unwraps said
phase difference image by replacing wrapped pixels in said phase
difference image with pixels in said modulated phase difference
image plus an integer multiple of .pi..
30. The system of claim 17, wherein said processor compares said
modulated phase difference image to said phase difference image by:
defining image segments in said phase difference image, defining
image segments in said modulated phase difference image; and
determining areas where the image segments in said phase difference
image overlap the image segments in said modulated phase difference
image.
31. The system of claim 30, wherein said processor unwraps said
phase difference image by replacing wrapped pixels in said
overlapping areas of said phase difference image with pixels in
said modulated phase difference image plus an integer multiple of
.pi..
32. The system of claim 31, wherein said processor computes said
integer multiple of .pi. as a function of the average difference
between values of pixels in said phase difference image and pixels
in said modulated phase difference image in the overlapping
area.
33. The system of claim 30 wherein said first defining step
includes: masking out pixels located near said one or more wraps of
said phase difference image to yield said image segments; and
wherein said second defining step includes: masking out pixels
located near said one or more wraps of said modulated phase
difference image to yield said image segments.
34. A computer-readable medium including a computer program for
processing digital images, said computer program including: a first
code section for acquiring a phase difference image which includes
one or more wraps; a second code section for creating a modulated
phase difference image from said phase difference image; a third
code section for comparing said modulated phase difference image to
said phase difference image to locate areas in said phase
difference image to be unwrapped; and a fourth code section for
unwrapping said phase difference image based on the overlapping
areas located in said comparing step.
Description
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention generally relates to processing images, and more
particularly to a system and method for unwrapping a phase
difference image in order to produce an image of improved quality
and information content.
2. Description of the Related Art
Computed imaging systems are employed in a wide variety of
applications, including medical, astronomy and terrain analysis.
The images produced by these systems often contain features known
as phase wrap. These features diminish the quality of the image and
therefore information content which might otherwise be discernable
if the features were not present. While the concept of phase wrap
is explained below in the specific context of a magnetic resonance
imaging (MRI) system, those skilled in the art are aware that phase
wrap may occur in other imaging modalities including computer
tomography, ultrasound, synthetic aperture radar, and even radio
astronomy.
Magnetic Resonance Imaging (MRI) is used to obtain digital images
of the internal structure of an object (e.g., the human body)
having substantial populations of atomic nuclei that are
susceptible to nuclear magnetic resonance (NMR) phenomena. In MRI,
a strong magnetic field is used to polarize nuclei in the object.
These nuclei are then excited by a radio frequency (RF) signal at a
particular NMR frequency. By spatially distributing the localized
magnetic fields, and then analyzing the resulting RF responses, an
image of relative NMR responses as a function of the location of
the nuclei may be generated. Additional processing will allow this
image to be displayed on a monitor for analysis by a doctor.
The excitation frequency may be defined by the Larmor relationship,
which states that the angular frequency, .omega..sub.0, of the
precession of the nuclei is the product of the magnetic field,
B.sub.0, and the so-called magnetogyric ratio, .gamma., a
fundamental physical constant for each nuclear species:
Accordingly, by superimposing a linear gradient field, B.sub.z =Z
G.sub.z, on the static uniform field, B.sub.0, which defined Z
axis, for example, nuclei in a selected X-Y plane can be excited by
a proper choice of the frequency spectrum of the transverse
excitation field applied along the X or Y axis. Similarly, a
gradient field can be applied in the X-Y plane during detection of
free induction decay signals to spatially localize these signals in
the plane. The angle of nuclei spin flip in response to an RF pulse
excitation is proportional to the integral of the pulse over
time.
It is well known that the magnetic resonance phase can serve as a
measure of some physical quantity. Depending on the pulse sequence,
the MR phase can, for example, represent the main B.sub.0 field
inhomogeneity which corresponds to phase wrap in the output
image.
In order to improve image quality, phase unwrapping is often
performed. Phase unwrapping refers to the process of determining
the absolute phase of a complex signal given the measurement of its
principal phase value. More succinctly, since the phase angle of a
complex number is unambiguous only between -.pi. and +.pi., the
phase of an image signal cannot be unambiguously determined from
its argument.
In the context of an MRI system, phase unwrapping is a necessary
tool for performing three-point Dixon water and fat separation and
can be used to increase the dynamic range of phase contrast MR
velocity measurements. Phase unwrapping has also been shown to be
important in the context of other systems, such as synthetic
aperture radar systems. See, for example, U.S. Pat. No.
6,011,625.
Various approaches have been proposed for performing phase
unwrapping. One approach is based on a least-squares algorithm
which determines the phase surface which best fits the ensemble of
pixel-to-pixel phase differences over an interferogram. If
inconsistencies are present, the least-squares process attempts to
minimize deleterious effects by minimizing the residual fitting
error.
Other approaches are based on a path-following algorithm. This
algorithm numerically integrates the pixel-to-pixel phase
differences over an interferogram, in the process of either
avoiding or minimizing inconsistencies by selecting paths where
error is minimized.
Another approach used specifically in MRI systems involves a
combination of modeling the static magnetic field using polynomial
functions as a guided phase unwrapping by region-growing. Such an
approach is disclosed, for example, in U.S. Pat. No. 6,263,228.
The phase unwrapping approaches discussed above are either locally
applied or remove a low-order approximation of the phase difference
image in an effort to make the remaining high-order image
wrap-free. By removing low frequencies from an image, some global
information is taken into account but the assumption that the
remaining high frequencies do not include any phase wraps is
frequently incorrect, especially in so-called open MRI systems, and
this is true even of geometrically simple phantoms. These
techniques do not take into account global information without
making a priori assumptions.
Local methods use nearest-neighbor pixels to determine whether a
pixel should be unwrapped. Methods of this type are highly
sensitive to phase errors. For example, a single pixel with an
incorrect phase can cause a wrap to be streaked across the entire
image. Local techniques which demonstrate this sensitivity include
recursive routines and the Ahn technique, the latter of which
streaks when applied column-by-column to two-dimensional phase
difference images even when a little noise is present.
Open MRI systems are especially susceptible to image degradation
caused by phase errors. Open MRI systems generate phase difference
images which are more difficult to unwrap than tranditional
cylindrical systems. In particular, the lower field strengths
produced by these systems have degraded signal-to-noise ratio in
the 0.7T OpenSpeed MRI system and the 0.5T Profile system compared
to 1.5T cylindrical systems. Furthermore, fields generated by open
MRI systems tend to be less homogenous than cylindrical systems and
therefore generate phase difference images with many more wraps to
be undone. Additionally, signal-to-noise is far worse in open MRI
systems, which produce a larger number of phase errors. Because
local unwrapping approaches look only at nearest neighbors when
determining whether to unwrap a pixel, they are slow, extremely
sensitive to phase errors, and therefore inadequate when applied to
open MRI.
Conventional phase unwrapping approaches have also proven
inadequate when applied to digital images in which noise is
present. For example, because the measurements are corrupted, it is
simply impossible to unwrap the image so the all nearest-neighbor
pixel differences are smaller than .pi..
In view of the foregoing considerations, it is clear that there is
a need for an improved method for unwrapping phase difference
images including those in which noise is present, and more
specifically one which may be applied more efficiently and with
fewer errors compared with conventional methods.
SUMMARY OF THE INVENTION
The present invention is a system and method for processing digital
images more efficiently and with fewer errors than conventional
methods. The invention is especially well suited to processing
digital images containing noise. The method includes acquiring a
phase difference image which includes one or more wraps, creating a
modulated phase difference image from the phase difference image,
comparing the modulated phase difference image to the phase
difference image to locate areas in said phase difference image to
be unwrapped, and unwrapping the phase difference image based on
the areas located in the comparing step. The modulated phase
difference image may be created by rotating the phase difference
image by a predetermined angle, and then registering the pixels in
the rotated image so that values of the pixels lie within a desired
phase range. The desired phase range may equal, for example, a
phase range within which pixels of the phase difference image
reside. The unwrapping step includes replacing wrapped pixels in
the phase difference image with pixels in the modulated phase
difference image.
The system of the present invention includes an imaging device, a
storage unit for storing an image from the imaging device, and a
processor for processing digital images in accordance with the
method of the present invention. The processor may perform the
method under control of a computer program stored in a memory unit
of the system. The various images generated by the invention may be
displayed on a monitor or other output device.
The system and method of the present invention is advantageous in a
number of respects. One advantage results from the replacement
step. Specifically, replacing pixels in the phase difference image
with pixels in the modulated phase difference image will have a
smoothing effect which will cause the wrapped pixels in the phase
difference image to become unwrapped. This is because the
replacement pixels in the modulated phase difference image
represent rotated pixels in the phase difference image, which
suffer no wraps near the phase wrap in the original image. As a
result, an image of improved quality and information content is
produced.
Further, the image segmentation steps of the invention may be
applied to remove inconsistent pixels from the region to be
unwrapped. In so doing, phase errors that would severely corrupt
results of local phase unwrapping routines are advantageously
eliminated. Another advantage is that the method of the present
invention takes a global approach to phase unwrapping. This will
allow AutoShim to be implemented in an open MRI system, and will
make AutoShim more effective in traditional cylindrical MRI
systems. Conventional methods cannot achieve these advantages
because they are locally applied. The invention also may be applied
to a wide variety of images, including magnetic resonance images
derived from both cylindrical and open MRI systems, computed
tomography images, X-ray images, ultrasound images, and images
derived from a synthetic aperture radar system. These and other
advantages and features of the invention are described in greater
detail in the discussion which follows.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a flow diagram showing steps included in one embodiment
of a method for processing digital images in accordance with the
present invention.
FIGS. 2A-2D show various stages in the development of a masked
phase difference image, where FIG. 2A shows an MR magnitude image,
FIG. 2B shows an MR phase difference image, FIG. 2C shows a
magnitude mask, and FIG. 2D shows a masked phase difference
image.
FIG. 3 is a flow diagram showing additional steps included in the
aforementioned embodiment of the method of the present
invention.
FIG. 4A shows an example of how a phase difference image
.phi..sub.meas may be segmented in accordance with the present
invention, and FIG. 4B shows an example of how a modulated phase
difference image .phi..sub.mod may be segmented in accordance with
the present invention.
FIG. 5 shows an example of an image segmentation mask which may be
used in association with the phase difference image shown in FIG.
2B.
FIGS. 6A and 6B respectively show segmented versions of the phase
difference and modulated phase difference images .phi..sub.meas and
.phi..sub.mod in accordance with the present invention, and FIG. 6C
shows segment numbers superimposed on the modulated phase
difference image shown in FIG. 6B.
FIG. 7 is a diagram showing overlapping image segments created
between the phase difference image and the modulated phase
difference image generated in accordance with the present
invention.
FIG. 8 is a diagram showing a first image segment unwrapped in
accordance with the present invention.
FIG. 9 is a diagram showing another image segment unwrapped in
accordance with the present invention.
FIG. 10 is a diagram showing another image segment unwrapped in
accordance with the present invention.
FIG. 11 is a diagram showing another image segment unwrapped in
accordance with the present invention.
FIG. 12 is a diagram showing another image segment unwrapped in
accordance with the present invention.
FIG. 13 is a diagram showing one embodiment of a system for
processing digital images in accordance with the present
invention.
DETAILED DESCRIPTION OF THE INVENTION
The present invention is a system and method for processing digital
images, and more specifically for unwrapping a phase difference
image produced, for example, from two original images. The phase
difference image may be any one of a magnetic resonance image, a
computed tomography image, an ultrasound image, an X-ray image, an
astronomy-related image, an image generated by a synthetic aperture
radar system, or the image may be any type of other phase
difference image which requires processing for information
recovery. The invention is especially well suited to unwrapping
images generated by an open MRI system, however the invention is
not in any way intended to be limited in this manner.
Referring to FIG. 1, an embodiment of the method of the present
invention includes as an initial step acquiring two phase images.
(Block 1). The two phase images may be obtained using known
techniques, which, for example, may include scanning a particular
location of a patient's body with a medical imaging machine,
scanning a particular area with a synthetic aperture radar, or
using various other imaging systems.
A second step includes generating a phase difference image from the
two phase images acquired in the initial step. (Block 2). The phase
difference image may be measured as:
wherein .phi..sub.meas corresponds to a measured phase difference
image which lies in a phase range of between -.pi. and +.pi.. In
equation (1), mod is a function which reduces .phi. (taking on all
real values between -.infin. and +.infin.) to a related function
.phi..sub.meas, which takes on values between -.pi. and +.pi. only.
By way of example, if (f+2.pi.) mod 2.pi.=f where f is any
function, then (3+2.pi.) mod 2.pi.=3. A phase difference image
according to this equation may be produced using conventional
techniques.
One such technique involves varying an imaging parameter between
the two phase images, so that the respective phases of those images
are different. For example, in phase contrast angiography (also
known as phase mapping) where flow velocity along an axis is to be
measured, the value of the first gradient moment along the axis is
varied to produce two different data sets. One of the phase images
is then subtracted from the other, on a pixel-by-pixel basis, to
provide the phase difference image.
Another technique, applied in MRI applications, creates a phase
difference image by taking two magnetic resonance images with
different gradient echo times (TEs), so that the images have the
same magnitudes but different phases:
When the natural log (ln) of the ratio of the above equations is
taken and then divided by .DELTA.TE, the phase difference image,
.phi.(x), is recovered as:
Because the magnitude of each pixel in (im2/im1) is identically 1,
it may be said that the magnitude, or intensity image, has been
stripped away.
In performing the foregoing MRI-based technique, it may be
advantageous to generate the phase difference image using a mask in
order to remove noise. The reason for this is as follows. MRI
images of patients often contain regions that are "air" therefore
produce no MRI signal. Pixels in these regions have wildly varying
phases which are physically meaningless. In accordance with one
aspect of the invention, an MR magnitude image may be used to
create an image mask which throws out all pixels with magnitude
image values below a given threshold. This resulting masked image
may then be used to perform the patching process in accordance with
subsequent steps of the method, to be discussed in greater detail
below.
The generation of a masked image is illustratively shown in the
images of FIGS. 2A-2D. FIG. 2A shows an MR magnitude image with
image values lying in the range of 0 to 2.times.10.sup.5. FIG. 2B
shows a phase difference image containing noise in regions of low
magnitude. FIG. 2C shows a magnitude mask having only those pixels
in the MR magnitude image which lie above some threshold (e.g., max
(magnitude image)/4)). The pixels in the magnitude mask
corresponding to the pixels in the magnitude image which satisfy
the threshold condition are set to 1; all other pixels are given a
value of 0. FIG. 2D shows a masked phase difference image,
generated by taking a pixel-by-pixel product of the magnitude mask
shown in FIG. 2C with the phase difference image shown in FIG. 2B.
As is evident from FIG. 2D, most of the "noisy" pixels have been
removed by the mask. Those skilled in the art can appreciate that
other techniques may be used for generating the phase difference
image processed in accordance with the present invention.
The phase difference image produced from the foregoing steps may
have one or more phase wraps which degrade image quality and
information recovery. The method of the present invention takes the
following steps to remove these effects.
A third step includes generating a modulated phase difference image
from the phase difference image generated in the second step.
(Block 3). In accordance with the present invention, the modulated
phase difference image is generated by rotating a phase angle of
the phase difference image by a predetermined angle, which lies
within a range of between 0 and 2.pi. but preferably corresponds to
.pi.. Rotating the phase difference image in this manner will allow
unwrapped pixels located near an area of wrapped pixels to be
substituted for the wrapped pixels in that area. This substitution,
or patching process, will result in smoothing the area where the
wrapped pixels are located, thereby improving the information
content at that area and thus the overall quality of the image.
In mathematical terms, the phase difference image may be modulated
according to the following equation:
where .phi..sub.mod is the modulated phase difference image,
.phi..sub.meas is the phase difference image, and .theta. is the
predetermined angle of rotation. When .theta.=.pi. in equation (2),
we therefore have by construction the following equation:
.phi..sub.mod =.phi..sub.meas.+-..pi. where .phi..sub.meas
.di-elect cons.[-.pi.,+.pi.), or equivalently
-.pi..ltoreq..phi..sub.meas.ltoreq.+.pi.. Also, .phi..sub.mod
.di-elect cons.[-.pi.,+.pi.), or equivalently
-.pi..ltoreq..phi..sub.mod.ltoreq.+.pi..
A fourth step is performed after the phase difference image has
been rotated. In the fourth step, the phases of the pixels in the
rotated image, .phi..sub.mod, may be corrected to lie within the
phase range of the phase difference image. (Block 4). The phase
range is between -.pi. and +.pi.. Correction to within this range
may be accomplished, for example, by subtracting 2.pi. from all
pixels in the rotated image which exceed a phase of .pi..
A fifth step includes comparing the modulated phase difference
image, .phi..sub.mod, to the phase difference image,
.phi..sub.meas, to locate areas in the phase difference image to be
unwrapped. (Block 4). Referring to FIG. 3, this comparing step may
include partitioning the phase difference image into a number of
image segments (Block 5a), and then performing a similar
partitioning for the modulated phase difference image (Block 5b).
The number of image segments may be two or greater, and the phase
difference image and the modulated phase difference image may be
partitioned into different numbers of image segments.
FIGS. 4A and 4B show an MRI-specific example of the way in which
the phase difference and modulated phase difference images may be
partitioned into segments in accordance with the present invention.
In FIG. 4A, the phase difference image, which is in the shape of a
convex collection of pixels, is schematically partitioned into four
image segments labeled Segments 1A through 4A. In FIG. 4B, the
modulated phase difference image, which has exactly the same shape,
is schematically partitioned into six image segments labeled
Segments 1B through 6B. The image segments are numbered in no
particular order and equally numbered segments have different
coverage areas, although those areas may have overlapping pixels.
Furthermore, while a convex shape is shown, the shape of the phase
difference and modulated phase difference images may be any shape
including those which are not convex.
The masked phase difference image and the modulated phase
difference image may be segmented into unwrapped regions. This may
be accomplished by "masking out" pixels located near wraps. The
location of the wraps may be determined using a standard high-pass
filter, and "wrapped" pixels may be identified as pixels whose
values differ from any one of their nearest neighbors by some
threshold amount. The threshold amount may be, for example,
.pi./2=25% of the 2.pi. phase range. Using this standard, only
pixels with values differing by .pi./2 from one of its nearest
neighbors are masked out. This choice of threshold is not unique
and can be altered without significantly changing the invention. It
is preferable to choose a small threshold so that a large number of
pixels will be masked out. This is beneficial because pixels
suffering large errors due to noise are masked out.
FIG. 5 shows an example of an image segmentation mask which may be
used in association with the phase difference image shown in FIG.
2B. The image which resulted from applying the segmentation mask to
the phase difference image is shown in FIG. 2D. By using this mask,
the phase wraps in each individual segment of the image may be
completely removed. FIGS. 6A and 6B respectively show segmented
versions of the images .phi..sub.mod and .phi..sub.meas in
connection with this example. FIG. 6C shows segment numbers
superimposed on the modulated phase difference image shown in FIG.
6B.
Returning to FIG. 3, the comparing step of the invention further
includes determining areas where the image segments in the phase
difference image overlap the image segments in the modulated phase
difference image. (Block 5c). FIG. 7 shows an example of how these
overlapping areas may be determined. In this figure, area 1A-1B
corresponds to an area where image segment 1A in the phase
difference image overlaps image segment 1B in the modulated phase
difference image; area 1A-2B corresponds to an area where image
segment 1A in the phase difference image overlaps image segment 2B
in the modulated phase difference image; area 2A-2B corresponds to
an area where image segment 2A in the phase difference image
overlaps image segment 2B in the modulated phase difference image;
area 2A-5B corresponds to an area where image segment 2A in the
phase difference image overlaps image segment 5B in the modulated
phase difference image; area 4A-5B corresponds to an area where
image segment 4A in the phase difference image overlaps image
segment 5B in the modulated phase difference image; area 4A-6B
corresponds to an area where image segment 4A in the phase
difference image overlaps image segment 6B in the modulated phase
difference image; area 2A-3B corresponds to an area where image
segment 2A in the phase difference image overlaps image segment 3B
in the modulated phase difference image; area 3A-3B corresponds to
an area where image segment 3A in the phase difference image
overlaps image segment 3B in the modulated phase difference image;
and area 3A-4B corresponds to an area where image segment 3A in the
phase difference image overlaps with image segment 4B in the
modulated phase difference image. This step may be simultaneously
performed during the unwrapping step, which will now be
discussed.
A sixth step of the method includes unwrapping the phase difference
image based on the areas located in the comparing step. First, an
initial image segment in the phase difference image is selected,
which, for example, may correspond to image segment 1A in FIG. 4A.
This image segment is then used to form the first image segment in
the unwrapped phase difference image. More specifically, the
unwrapped phase difference image is initialized to be identically
zero except for pixels corresponding to selected image segment in
the phase difference image. This initial image segment is unwrapped
by construction, e.g., by removing all the wrapped pixels in the
selected image segment so that there are no longer any wraps in
this segment. The portion of the unwrapped phase difference image
which results after this initial step is illustratively shown in
FIG. 8, where shaded segment 1A corresponds to the first unwrapped
segment in the unwrapped phase difference image.
In a next step, an image segment in the modulated phase difference
image is selected which overlaps unwrapped image segment 2A in the
phase difference image. An overlapping image segment may be
identified, for example, using a computer program which performs
the comparison performed in the comparing step to determine these
overlapping segments. As an example, the overlapping image segment
identified by this program may be image segment 2B in the modulated
phase difference image shown in FIG. 4B. This overlapping area
corresponds to the area 2A-2B in FIG. 7.
Once this overlapping image segment is identified, pixels in the
phase difference image located in the overlapping image segment are
replaced by the pixels in image segment 2B of the modulated phase
difference image, plus an integer multiple of .pi.. This integer
multiple may be computed by comparing overlapping pixels in the
image segments as explained in the discussion which follows. The
result of this step is to produce unwrapped area 2A-2B as
illustratively shown in FIG. 9.
Replacing pixels in the phase difference image with pixels in the
modulated phase difference image plus an integer multiple of .pi.
will have a smoothing effect which will cause the wrapped pixels in
the phase difference image to become unwrapped. This is because the
replacement pixels in the modulated phase difference image
represent rotated pixels in the phase difference image, which
suffer no wraps near the phase wrap in the original image.
Therefore, it is easy to infer from the modulated phase difference
image, the amount by which these pixels should be shifted.
Iteratively performing pixel replacement (patching) in this manner
extends the unwrapped phase difference image without introducing
phase wraps. (Note that not all pixels in the original phase
difference image are necessarily unwrapped by this process. Some
may be left identically zero.)
The image resulting from the pixel replacement performed in the
foregoing steps may be referred to as the unwrapped phase
difference image, represented as .PHI..sub.uw. At this point,
however, only the portion of the phase difference image which
correspond to segments 1A-1B, 1A-2B, and 2A-2B in FIG. 7 are
considered unwrapped. In subsequent steps, successive iterations
are performed to unwrap the remaining portions of the phase
difference image. This involves filling the remaining portions with
unwrapped pixels until a final unwrapped phase difference image is
produced. These subsequent steps may be performed as follows.
In a next step, areas in the phase difference image which
correspond to image segments 2A-3B and 2A-5B in FIG. 7 are
successively or simultaneously unwrapped. This involves replacing
the pixels in the phase difference image located in areas 2A-3B and
2A-5B with pixels in the modulated phase difference image which are
also located in these areas plus an integer multiple of .pi.. The
result of this replacement is shown in FIG. 10, where areas labeled
2A-3B and 2A-5B are now considered to be unwrapped in
.PHI..sub.uw.
In a next step, areas in the phase difference image which
correspond to image segments 3A-3B and 4A-5B in FIG. 7 are
successively or simultaneously unwrapped. This involves replacing
the pixels in the phase difference image located in areas 3A-3B and
4A-5B with pixels in the modulated phase difference image which are
also located in these areas plus an integer multiple of .pi.. The
result of this replacement is shown in FIG. 11, where areas labeled
3A-3B and 4A-5B are now considered to be unwrapped in
.PHI..sub.uw.
In a next step, areas in the phase difference image which
correspond to image segments 3A-4B and 4A-6B in FIG. 7 are
successively or simultaneously unwrapped. This involves replacing
the pixels in the phase difference image located in areas 3A-4B and
4A-6B with pixels in the modulated phase difference image which are
also located in these areas plus an integer multiple of .pi.. The
result of this replacement is shown in FIG. 12, where areas labeled
3A-4B and 4A-6B are now considered to be unwrapped in .PHI..sub.uw.
While it is generally preferred that the order for unwrapping image
segments proceeds from largest to smallest, those skilled in the
art can appreciate that the order in which the image segments are
unwrapped may be varied as desired. For example, image segments
2A-5B, 4A-5B, and 4A-6B may be unwrapped before segments 2A-3B,
3A-3B, and 3A-4B.
Through this systematic, iterative pixel replacement approach, the
system and method of the present invention unwraps phase difference
images more efficiently and with fewer errors than conventional
methods. This is because the invention takes a global approach to
phase unwrapping which is extremely robust to noise. In contrast,
conventional methods are local in nature and therefore cannot
achieve these advantages.
In mathematical terms, and by way of example, the pixel replacement
steps discussed above may be performed in the following manner:
a) For a first segment in the phase difference image, initialize
.phi..sub.uw to be that segment surrounded by zeros and determine
the pixels that overlap between unwrapped phase difference image
.phi..sub.uw and the modulated phase difference image
.phi..sub.mod.
b) For each segment of .PHI..sub.mod containing pixels determined
in step a), compute .DELTA..phi., which is the average difference
between the values of the unwrapped phase difference image
.phi..sub.uw and this particular segment of the modulated phase
difference image .phi..sub.mod on the pixels determined in step a).
Ideally, .DELTA..phi. is an integer multiple of .pi., i.e.,
.DELTA..phi.=m.pi., for some integer m. In practice, .DELTA..phi.
may not be quite an integer multiple.
c) Compute the nearest integer, m, to which .DELTA..phi. is a
multiple of .pi., where m=round(.DELTA..phi./.pi.).
d) Replace pixels in .phi..sub.uw which are in the overlapping
segment of the phase difference image but which are not already
unwrapped with pixels having values of .phi..sub.mod +m.pi..
e) Repeat this pixel replacement process (steps b), c), and d)) for
all remaining overlapping segments that exist between the unwrapped
image and alternately the modulated phase difference image and
measured phase difference image.
FIG. 13 shows an embodiment of the system 100 for processing
digital images in accordance with the present invention. The system
includes an imaging device 101 for capturing a digital image
including any of the types previously described, a storage device
102 for storing the digital image, and a processor 103 for
processing the digital image in accordance with the steps of the
method of the present invention. The steps of the invention may be
performed by a computer program stored in a memory unit 104 of the
system. A display monitor 105 or other output device may also be
included to show the various images generated by the invention
including the final unwrapped phase difference image.
By taking this global approach to phase unwrapping, the system and
method of the present invention will allow AutoShim to be
implemented in an open MRI system, and will make AutoShim more
effective in traditional cylindrical MRI systems. This may be
understood as follows.
AutoShim is a correction step performed just before scanning a
patient. The primary purpose of AutoShim is to correct background
field inhomogeneities created by the patient. (The patient actually
perturbs the experimental setup.) When the background field has
relatively large inhomogeneity, then AutoShim also works to reduce
the background field inhomogeneity. HFO is such a system.
Furthermore, 0.7T open systems suffers from poor S/N compared to
conventional 1.5T magnets. This loss of S/N makes the phase
difference images extremely noisy, and combined with HFO's degraded
background homogeneity, forces a more sophisticated approach to
AutoShim.
Conventional Autoshim does not unwrap phase difference images and
only controls linear gradients. While these systems may estimate
linear components in the field from local information relatively
accurately, this estimation process is less than ideal because each
linear gradient is estimated independently from an average of many
local linear fits.
The system and method of the present invention will make Autoshim
more effective for systems suffering degraded S/N due to low field
strength, systems suffering severe background field inhomogeneity,
and also for systems suffering large susceptibility errors due to
particularly high field strength. The segmentation routine
eliminates noisy pixels, while the phase unwrapping increases the
range of field inhomogeneity that AutoShim can detect and
therefore, correct.
The system and method will also improve open MRI systems
significantly. Open MRI systems, such as OpenSpeed, use a quadratic
"z2" coil which requires the Autoshim's phase difference images to
be fit to a nonlinear function. Unwrapping phase difference images
in accordance with the present invention will allow a simultaneous
least-squares fit of all desired gradients (both linear and
nonlinear). This will enable the fitting of the nonlinear "z2"
coefficient and improve accuracy of the linear fits.
The present invention is also able to perform phase unwrapping of
an image which contains noise. The unwrapping procedure is
performed independent of noise levels. However, noisy data is
masked out during the segmentation step.
Other modifications and variations to the invention will be
apparent to those skilled in the art from the foregoing disclosure.
Thus, while only certain embodiments of the invention have been
specifically described herein, it will be apparent that numerous
modifications may be made thereto without departing from the spirit
and scope of the invention.
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